A285458 Expansion of Product_{k>=1} ((1 + x^k) / (1 - x^(4*k)))^k.

1, 1, 2, 5, 9, 17, 30, 54, 94, 161, 269, 449, 740, 1200, 1930, 3083, 4877, 7650, 11919, 18444, 28363, 43341, 65848, 99523, 149654, 223901, 333448, 494427, 729996, 1073408, 1572264, 2294389, 3336191, 4834261, 6981727, 10050944, 14424665, 20639641, 29447118

Offset

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..1000

Formula

a(n) ~ exp(1/12 + 3 * (13*Zeta(3))^(1/3) * n^(2/3) / 4) * (13*Zeta(3))^(7/36) / (2 * A * sqrt(3*Pi) * n^(25/36)), where A is the Glaisher-Kinkelin constant A074962.

Mathematica

nmax = 40; CoefficientList[Series[Product[((1+x^k)/(1-x^(4*k)))^k, {k, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A015128, A000041, A285445, A006950.

Cf. A156616, A000219, A285446, A285459.

Sequence in context: A133470 A129696 A082281 * A000569 A292168 A322304

Adjacent sequences: A285455 A285456 A285457 * A285459 A285460 A285461

Keyword

nonn

Author

Vaclav Kotesovec, Apr 19 2017

Status

approved